I use "Sum of Ratings," as I think you said you do, which provides a lot of flexibility. In my own case, I tell students that they get a perfect discussion grade when they get 8 points (you appear to use 10). Each post is worth up to 2 points each, so most students can get a perfect score with 4 posts. Not all students, for whatever reason, get 8 points. When they do, somewhat by definition, they have not made the full contribution.
So, their final grade in the gradebook (between 0 and 8 in my courses) I think does reflect students' contributions. Oh, I should mention a few things. I read and "rate" their posts regularly, telling them to watch their grade book. Then, after the due date, I have to manually enter a 0 into their grade book for any student who did not make a single post.
I am not sure when "Average of Rating" or "Count of Ratings" would be better than Sum of Ratings. But they are there for those who want to use them. In my courses, a discussion is rather casual, yet thoughtful. If a student simple writes "I agree with Serena" I provide only 1 of the 2 points, and I add my own post saying, "Please explain why?" So I am seeking a little bit of "quantity," or "engagements" along with some "thought."
I teach online college-level courses, and Moodle's discussion tool is great. When I used to teach face-to-face, and in a classroom, if I asked a question seldom would I get every student making four decent comments.
So, your need can be valid, but I wonder if you are making things too hard on yourself.